Learn Hardcore Korean: geu gwamok ganguineun maeju hwayoire jinhaengdwae. - That course’s lecture is held every Tuesday.

과목 means “course” or “subject” (e.g., Math, History).
강의 means “lecture” or “class session.”
You use 과목 강의 to specify “the lecture/lectures for that particular course.” In other words, 그 과목 tells you which course, and 강의 tells you it’s about the lecture(s) rather than, say, the textbook or the homework.

Why don’t we say 그 과목의 강의 with the genitive particle 의?

In everyday Korean, you can often drop 의 when two nouns are directly related.

그 과목 강의 (more colloquial)
그 과목의 강의 (more formal or explicit)
Both are correct, but native speakers frequently omit 의 to sound more natural and concise.

What role does the topic marker 는 play after 강의?

The particle 는 marks 강의 as the topic of the sentence—i.e., “As for the lecture…” It sets up what you’re going to say about it, which in this case is when it takes place. Without 는, the sentence would lose that topical emphasis.

Why is 매주 화요일에 used for “every Tuesday,” and could you say 매 화요일마다 instead?

매주 화요일에 literally means “on Tuesday of every week.” It’s the most common way to say “every Tuesday.”
매 화요일마다 also means “every Tuesday” but sounds a bit more emphatic or old-fashioned.
Both are grammatically correct; 매주 화요일에 is simply more neutral and widely used.

What does 진행돼 mean, and is it passive?

진행되다 means “to be conducted” or “to take place.”
In this sentence, it’s not exactly the passive of “someone conducts it.” Rather, it’s an intransitive usage meaning “the lecture takes place.”
So 진행돼 = “(it) is held” or “(it) goes on.”

Why does the verb end in -돼 instead of -돼요 or -됩니다?

Korean verbs in dictionary form end in -다, e.g., 진행되다.

진행돼 is the plain, declarative present tense (often used in writing or casual speech).
진행돼요 is the polite present tense.
진행됩니다 is the formal present tense.
Here the speaker chose the plain style (–돼) for a neutral, slightly informal tone.

Why is the particle 에 used after 화요일?

The particle 에 marks a point in time. Since 화요일 is a day of the week, you attach 에 to say “on Tuesday.” Without 에, the time expression would be incomplete.